An improved single variable first-order grey model

Grey system theory can effectively deal with incomplete and uncertain information. The grey model (GM) is the core of grey system theory, which collects available data to obtain internal regularity without using any assumptions. To further improve the precision of the prediction, this paper proposes an optimized GM(1,1) (OGM), which improves traditional GM(1,1) in two aspects: one is to improve the whitening equation by using the least square method; the other is to employ a technique of dynamic forecasting with recursive compensation by grey numbers of identical dimensions. The cases studies in population prediction and urban water demand prediction reveal that the improvement is definitely effective and the proposed OGM has not only greater precision but also higher stability than TGM.